This is my Build for Akali. Please read it before you rate it. She is my Main Character because she is a really good damage dealer and once she got her ultimate, she can either chase enemies to death or get away without taking too much damage.
I use this build for her and it works fine, here my stats (yeah, the last game sucked ^^)

Pro:

-Does a huge amount of damage.
-Can chase enemies really good.
-Has 3 Ulti Loads.
-Can harass really good.

Con:

-Is kinda squishy.
-Will be targeted first.
-Not many ways to farm effectively.

You may think: "WTF Rush Trinity Force?? Omg Downvote, what a Noob!", but there are many reasons why this works really well with Akali. First off, you can activate her Passive quickly if you buy Amplifying Tome and Long Sword, which is really useful. She then gets Spellvamp and a Bonus Magic Damage! The passive of Trinity Force is also really good for her, because the slow really helps chasing opponents. And, all in all, it gets her more run speed, damage, ability power and so on. What do you want more?

As Runes I choose Magic Penetration and Ability Power as main focus, but you can choose other Runes. However, as Quints I would recommend some for Ability Power, if you want to make more damage in the beginning I would recommend you flat runes. The extra health is really useful early game.

As Masteries I choose a 21-9-0 Runes, getting more Attack Power and Dodge Chance. That raises your Deathlyness and your Survivabilty is higher. Some Builds go 9-21-0, but I think if you play good, you don't need this many Defense Points.

Core Items:

Trinity Force

Your main Item, I already explained why. It raises nearly all your stats.

Hextech Gunblade

While the extra Damage and Ability Power is nice, the spellvamp and life steal rocks most! You can survive very long and even if you get ganked, your Twilight Shroud combined with Crescent Slash can save your ***.

Rylai's Crystal Scepter

I can't explain how important that Item is. It gives you a huge amount of HP and also gives you an additional slow with your abilities. The AP are also really nice.

Rabadon's Deathcap

I think I don't have to explain this item. Huge AP boost.... Do I have to say more?

Situational Items

Mejai's Soulstealer

BUY THIS ONLY IF YOU HAVE A GOOD RUN! It's very situational and if you die too often, it was just a gold-burn.

Void Staff

By this if you fight against a very tanky team. It also gives many AP.

Abyssal Mask

If you need some Magic Resistance because they got a fed caster.

Zhonya's Hourglass

If they got a fed AD Carry or Assassin like Talon

Your Main Harass- and Damgage skill will be Mark of the Assassin. Therefore this gets level 5 as soon as possible! Twilight Shroud can be used defensive and offensive, either to get invisible and run away (+ slowing your opponent) or to get in battle invisibly and deal as much damage as possible without getting too many damage. Always remember: Akali is kind of squishy and you will be focused when they see your damage! Crescent Slash is a descent farming Ability and it's good for dealing damage to multiple targets. The Ultimate, Shadow Dance, is a very special one, because you have 3 loads of it and it reloads every 25 seconds. It's one of the best chasing abilities ingame and with it you can even tower dive - hit opponent with Shadow Dance, if needed, a Mark of the Assassin, and quickly go out targetting an enemy Minion with Shadow Dance. If you do it right, the tower will hit you only once, but be sure you have enough HP for the case the tower hits you twice!

General Skill Sequence is:
Shadow Dance, Mark of the Assassin, [Auto-Hit], Crescent Slash, Mark of the Assassin and repeat!

My Summoner Spells are Ghost and Exhaust, because they are either good for chasing opponents, for switching lanes or for getting away.

Other possibilities are Ignite, Flash and Teleport, but I think the ones I chose are better because you can hunt them with your Ult instead of Ignite them and you can target an enemy Minion if you need to get away instead of Flash. Teleport can be good for ganks but how I said, I like to use Exhaust and Ghost.

Here a few situations that can happen, this section will be updated sometimes.

If you fight Karthus and he does his ult, don't be shy to hide under your Twilight Shroud. It gives you additional magic resistance and can save your ***.
If you get ganked, use Twilight Shroud and Shadow Dance to get away. This works best if you work premate, for example if you run away and come near the dragon, tell your mate to do a CV or something like this so that you can Shadow Dance there. Also works over walls to golems or Wraiths.
I can't explain how important Twilight Shroud is to escape ganks or something.

...

Akali is a really good Damage Dealer with a Focus on Ability Power. But never forget: She can be killed.
The opponents you will hate are Twitch, Evelynn and Teemo (everyone hates Teemo, but you will hate him most). Nearly all other players can fall for you - if you play right. And with the Tips I gave you, you can have success.

It needs a littlebit skill to play Akali, but if you can play her, it's really easy to get many kills.

Detailed How-to-play guide (only if people like my build)
Build in Picture of Stats
Maybe make a video
General corrections